Hadronic light-by-light contribution to the muon $g-2$ from holographic QCD with solved $U(1)_A$ problem

TL;DR

This paper uses a holographic QCD model incorporating the U(1)_A anomaly to accurately compute the hadronic light-by-light scattering contributions to the muon g-2, aligning well with the Standard Model.

Contribution

It introduces a minimal hard-wall AdS/QCD extension with U(1)_A anomaly to improve calculations of muon g-2 contributions, including axial vector mesons.

Findings

Accurate fits for η and η' masses and decay rates.

Muon g-2 contributions consistent with Standard Model.

Updated predictions for axial vector contributions.

Abstract

We employ the comparatively minimal extension of hard-wall AdS/QCD due to Katz and Schwartz which takes into account the U(1)$_A$ anomaly for computing hadronic light-by-light scattering contributions of pseudoscalar and axial vector mesons to the anomalous magnetic moment of the muon $a_\mu$. By including a gluon condensate as one extra tunable parameter besides those fixed by $f_\pi$ and the pion, kaon, and rho masses, we obtain remarkably accurate fits for $\eta$ and $\eta'$ masses and their decay rates to photons, leading to $a_\mu$ contributions in complete agreement with the Standard Model result by the Muon $g-2$ Theory Initiative. Turning to the less well understood axial vector contributions, we update our previous predictions obtained in flavor-symmetric hard-wall AdS/QCD models without U(1)$_A$ breaking.